Coefficient Rings of Numerical Semigroup Algebras

TL;DR

This paper explores the properties of numerical semigroup rings from a relative perspective, focusing on how algebraic, arithmetic, and set-theoretic features behave within equi-gcd numerical semigroup algebras.

Contribution

It introduces the concept that properties of numerical semigroup rings can be understood through the lens of equi-gcd numerical semigroup algebras, extending previous flatness-based insights.

Findings

Algebraic properties are preserved under equi-gcd numerical semigroup algebras.

Arithmetic properties of numerical semigroup rings are characterized within this framework.

Set-theoretic properties are also shown to be properties of equi-gcd numerical semigroup algebras.

Abstract

Numerical semigroup rings are investigated from the relative viewpoint. It is known that algebraic properties such as singularities of a numerical semigroup ring are properties of a flat numerical semigroup algebra. In this paper, we show that arithmetic and set-theoretic properties of a numerical semigroup ring are properties of an equi-gcd numerical semigroup algebra.